Recent experimental and theoretical obsevations suggest that production of (multi-)strange hadrons and charged hadrons in (non-)deformed nuclei is a complex physical process. The properties of charged hadrons produced in deformed nucleus collisions at RHIC and LHC energies contradict many of the theoretical models result including two-component Monte Carlo Glauber model. Unlike light hadrons, the production mechanism of (multi-)strange hadrons is quite involved as they do not simply produce according to their statistical weights as described in grand canonical ensemble. In recent past, several efforts have been made to provide a mechanism for (non-)strange hadron production in symmetric and asymmetric heavy ion collision experiments. However, an unified theoretical or simulation model which reproduce the multiplicity distribution of (multi-)strange hadrons alongwith multiplicity of charged hadrons is still lacking. In this article, we have used HYDJET++ model to calculate multiplicity distribution of (non-)strange hadrons with various control parameter in symmetric collision of (non-)deformed nuclei at RHIC and LHC energies. We have calculated the pseudorapidity distribution, transverse momentum distribution and elliptic flow distribution of charged hadrons with different control parameters.We observed that HYDJET++ along with certain parameters can adequately provide a unified model for light as well as strange hadron production in various type of collisions.